Properties

Label 4.4.19429.1-15.1-f
Base field 4.4.19429.1
Weight $[2, 2, 2, 2]$
Level norm $15$
Level $[15, 15, w^{2} - 2w - 5]$
Dimension $8$
CM no
Base change no

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Base field 4.4.19429.1

Generator \(w\), with minimal polynomial \(x^{4} - x^{3} - 7x^{2} - x + 5\); narrow class number \(1\) and class number \(1\).

Form

Weight: $[2, 2, 2, 2]$
Level: $[15, 15, w^{2} - 2w - 5]$
Dimension: $8$
CM: no
Base change: no
Newspace dimension: $25$

Hecke eigenvalues ($q$-expansion)

The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:

\(x^{8} - 5x^{7} - 30x^{6} + 161x^{5} + 234x^{4} - 1406x^{3} - 793x^{2} + 3840x + 1696\)

  Show full eigenvalues   Hide large eigenvalues

Norm Prime Eigenvalue
3 $[3, 3, -w^{3} + 2w^{2} + 5w - 3]$ $\phantom{-}1$
5 $[5, 5, w]$ $\phantom{-}1$
7 $[7, 7, -w^{3} + 2w^{2} + 4w - 3]$ $\phantom{-}e$
13 $[13, 13, -w^{2} + w + 4]$ $-\frac{455}{35303}e^{7} + \frac{4572}{35303}e^{6} + \frac{2828}{35303}e^{5} - \frac{119576}{35303}e^{4} + \frac{174499}{35303}e^{3} + \frac{572784}{35303}e^{2} - \frac{931225}{35303}e - \frac{355608}{35303}$
13 $[13, 13, -w^{3} + 2w^{2} + 5w - 2]$ $-\frac{753}{35303}e^{7} + \frac{1980}{35303}e^{6} + \frac{21517}{35303}e^{5} - \frac{50395}{35303}e^{4} - \frac{142919}{35303}e^{3} + \frac{189959}{35303}e^{2} + \frac{286095}{35303}e + \frac{252398}{35303}$
16 $[16, 2, 2]$ $-\frac{3049}{141212}e^{7} - \frac{5907}{141212}e^{6} + \frac{74107}{70606}e^{5} + \frac{153287}{141212}e^{4} - \frac{1089199}{70606}e^{3} - \frac{463695}{70606}e^{2} + \frac{8616513}{141212}e + \frac{996463}{35303}$
17 $[17, 17, -w + 2]$ $\phantom{-}\frac{279}{70606}e^{7} + \frac{5033}{70606}e^{6} - \frac{13902}{35303}e^{5} - \frac{134073}{70606}e^{4} + \frac{273809}{35303}e^{3} + \frac{345476}{35303}e^{2} - \frac{2112789}{70606}e - \frac{386146}{35303}$
19 $[19, 19, -w^{3} + 2w^{2} + 3w - 2]$ $-\frac{4869}{141212}e^{7} + \frac{12381}{141212}e^{6} + \frac{79763}{70606}e^{5} - \frac{325017}{141212}e^{4} - \frac{740201}{70606}e^{3} + \frac{752479}{70606}e^{2} + \frac{4891613}{141212}e + \frac{323128}{35303}$
27 $[27, 3, w^{3} - 3w^{2} - 4w + 7]$ $\phantom{-}\frac{2567}{141212}e^{7} - \frac{13923}{141212}e^{6} - \frac{28073}{70606}e^{5} + \frac{374427}{141212}e^{4} + \frac{10575}{70606}e^{3} - \frac{984723}{70606}e^{2} + \frac{1309121}{141212}e + \frac{436544}{35303}$
31 $[31, 31, w^{3} - 3w^{2} - 3w + 7]$ $\phantom{-}\frac{1170}{35303}e^{7} - \frac{1670}{35303}e^{6} - \frac{42575}{35303}e^{5} + \frac{40187}{35303}e^{4} + \frac{464123}{35303}e^{3} - \frac{111186}{35303}e^{2} - \frac{1640050}{35303}e - \frac{719604}{35303}$
31 $[31, 31, -w^{3} + w^{2} + 6w + 1]$ $-\frac{6451}{70606}e^{7} + \frac{26105}{70606}e^{6} + \frac{83050}{35303}e^{5} - \frac{685375}{70606}e^{4} - \frac{387417}{35303}e^{3} + \frac{1629298}{35303}e^{2} + \frac{893443}{70606}e - \frac{418402}{35303}$
41 $[41, 41, w^{2} - w - 1]$ $\phantom{-}\frac{1543}{70606}e^{7} + \frac{9867}{70606}e^{6} - \frac{52590}{35303}e^{5} - \frac{254077}{70606}e^{4} + \frac{946280}{35303}e^{3} + \frac{653654}{35303}e^{2} - \frac{8114929}{70606}e - \frac{1599316}{35303}$
43 $[43, 43, 2w^{3} - 5w^{2} - 6w + 4]$ $\phantom{-}\frac{13195}{141212}e^{7} - \frac{26679}{141212}e^{6} - \frac{217521}{70606}e^{5} + \frac{678767}{141212}e^{4} + \frac{2041503}{70606}e^{3} - \frac{1280071}{70606}e^{2} - \frac{13381107}{141212}e - \frac{1305172}{35303}$
47 $[47, 47, -w^{3} + 2w^{2} + 5w - 1]$ $\phantom{-}\frac{455}{35303}e^{7} - \frac{4572}{35303}e^{6} - \frac{2828}{35303}e^{5} + \frac{119576}{35303}e^{4} - \frac{174499}{35303}e^{3} - \frac{572784}{35303}e^{2} + \frac{895922}{35303}e + \frac{496820}{35303}$
53 $[53, 53, -w - 3]$ $-\frac{521}{141212}e^{7} + \frac{3761}{141212}e^{6} - \frac{3269}{70606}e^{5} - \frac{86721}{141212}e^{4} + \frac{255743}{70606}e^{3} + \frac{152661}{70606}e^{2} - \frac{3105343}{141212}e - \frac{322616}{35303}$
53 $[53, 53, -w^{3} + 3w^{2} + 3w - 6]$ $\phantom{-}\frac{1132}{35303}e^{7} + \frac{3212}{35303}e^{6} - \frac{60805}{35303}e^{5} - \frac{89597}{35303}e^{4} + \frac{959826}{35303}e^{3} + \frac{610977}{35303}e^{2} - \frac{3995836}{35303}e - \frac{2177872}{35303}$
59 $[59, 59, 2w^{2} - 3w - 6]$ $\phantom{-}\frac{6527}{70606}e^{7} - \frac{35869}{70606}e^{6} - \frac{64820}{35303}e^{5} + \frac{944943}{70606}e^{4} - \frac{108286}{35303}e^{3} - \frac{2316158}{35303}e^{2} + \frac{3747523}{70606}e + \frac{1594246}{35303}$
59 $[59, 59, w^{3} - w^{2} - 7w - 3]$ $-\frac{493}{35303}e^{7} + \frac{9454}{35303}e^{6} - \frac{15402}{35303}e^{5} - \frac{249360}{35303}e^{4} + \frac{670202}{35303}e^{3} + \frac{1259644}{35303}e^{2} - \frac{3216405}{35303}e - \frac{1602058}{35303}$
79 $[79, 79, 2w^{3} - 4w^{2} - 8w + 3]$ $\phantom{-}\frac{10815}{70606}e^{7} - \frac{51645}{70606}e^{6} - \frac{123225}{35303}e^{5} + \frac{1335063}{70606}e^{4} + \frac{238493}{35303}e^{3} - \frac{3005456}{35303}e^{2} + \frac{2201885}{70606}e + \frac{429834}{35303}$
79 $[79, 79, w^{2} - 2w - 1]$ $-\frac{3979}{141212}e^{7} + \frac{24387}{141212}e^{6} + \frac{49841}{70606}e^{5} - \frac{670711}{141212}e^{4} - \frac{189675}{70606}e^{3} + \frac{1891483}{70606}e^{2} - \frac{15389}{141212}e - \frac{701726}{35303}$
Display number of eigenvalues

Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
$3$ $[3, 3, -w^{3} + 2w^{2} + 5w - 3]$ $-1$
$5$ $[5, 5, w]$ $-1$